\textbf{Sound Propagation}. The theory of wave propagation is well established in classic physics and many simulation methods are proposed in the context of computational physics, acoustics, architecture, and computational electromagnets.
The propagation of sound is governed by partial differential equation (PDE), or Huygens Principle, which states that \emph{"every point of a wave frontier can be considered as source of secondary wavelets known as sub-source which spreads out in all directions."} 
%There has been a lot of research about PDE and wave simulation in the context of applied math and computational physics, and in conjunction with computational electromagnetics, a lot of simulation methods adapting to different circumstances have been proposed, including TLM method \cite{UKV}.

An overview of computational methods in acoustics as introduced as follows:

\begin{itemize}
  \item \emph{Finite Difference Method} is the most classic numerical analysis technique used to solve PDE. PDE is discretized by replacing the derivatives with formulas deducing from the Taylor series. \emph{Finite Element Method} is different from finite difference method for its irregular mesh deposition adapting to complex boundaries.
    %It's pointed out that every wavelength should have 6-10 samples to give an accurate result \cite{Mehra201283}, which makes it very costly.
  %\item \emph{Finite Element Method}
    %The difference between finite element method and finite difference method is that the former use irregular mesh adapting to complex boundaries.
  \item \emph{Cellular Automata Method} updates all cells simultaneously, and the update of a cell is determined only by cells in its vicinity \cite{UKV}. Cellular automata method in nature is also a numerical method, but it is more efficient than solving differential equation and suitable to be implemented on the computer.
  \item \emph{TLM method}
    Transmission Line Matrix (TLM) method is very popular in electromagnetic wave propagation, and it's also applied to the simulation of sound wave. TLM method is based on cellular automata and inherits its high efficiency, which is the primary concern to choose a model here. TLM Model consists of a mesh of interconnected nodes. As shown in Fig1. Based on Huygens' principle, the energy of a directional incident pulse with an amplitude scatters to four directions.
    \begin{figure}[h]
    \centering
        \includegraphics[width=7cm]{images//TLM.jpg}
        \caption{An illustration of TLM method.}
    \label{}
    \end{figure}
  \item \emph{Raytracing Method}
    The raytracing method has draw a lot of attention from computer graphics. It is assumed that sound propagates as rays of energy quanta, and this is also known as beam tracing in computer graphics. The advantage of this method is that it's the least computationally expensive one among all methods.
    One drawback of this method is the inability of simulating low-frequency phenomena such as diffraction. So it's incapable of dealing with the perception problem of corner case in the  section 5. So it's suitable for high-frequency simulation.
\end{itemize}

\textbf{Sound Localization}.
%Since the accurate sound rendering and propagation is introduced to computer graphics just recent years, most of the relevant work is in the context of robotics instead of graphics.
%The research group in UNC has a series of publications and projects in the intersection of robotics and graphics.


Sound source localization (SSL) draws huge attention from biomedical scientists, physiologists, engineers and computer scientists. Distance estimate can be achieved by measuring sound intensity and spectrum, and during the process a prior knowledge about the source's characteristics of radiation is needed \cite{AISL}.
The mechanism of human's ability to determine the location of nearby sound sources is not fully understood \cite{MKD}. Human depends on a number of anatomical properties of the human auditory system, including interaural intensity difference (IID), interaural time difference (ITD), and directional sound filtering of the human body.
An artificial robust localization system demands different approaches \cite{AISL}, and often uses pressure sensors arrays.
%Nehorai and Paldi (1994) introduced a novel vector sensor,
In the area of robotics, one of the most widely used method for the passive localization of acoustic source is based on the measurement of the time delay of arrival (TDOA) of the source signal to receptor pairs \cite{650785}\cite{AISL}. By locating three sensors and recording the time difference of sound arriving, it's easy to calculate the position of sound source analytically. But it's very strange to assume that one agent has three "ears", and the method cannot be integrated with a low resolution sound propagation model because if the representation of sound grid is rough, the result of TDOA will be very inaccurate. For example, if the distance between two receptors pairs is 4, there is only 9 possible time delays (from -4 to 4).
Instead, our algorithm makes use of local sound packets information that the virtual human perceived to determine the direction and distance of the sound source, and it also provides a very simple way to judge the confidence of localization.

\textbf{Crowd Steering}.
%TODO: summarize the steering algorithsm using information of vision, sound, or any other modalities.
An introduction to crowd simulation can be found in the classic texts \cite{PAN}\cite{Tha}. Our work can be closely related to rule-based model, social force model, and geometrically-based local avoidance model.
\begin{itemize}
  \item \emph{Social force model} assumes virtual forces existing between pedestrians and wall, and then solves Newton's equation for each agent. Forces between agent include radial (repulsive) and tangential forces, which take psychological and physical factors into consideration and simulate interactions between people. Pelechano has proposed a revised version of social force \cite{P07}.
  \item \emph{Rule based model} describes each agent as an individual, and agent behaves according to its local perception of the virtual environment and through a set of basic rules.
        %and adopt a conservative approach to avoid collision.
        In Reynolds' seminal work \cite{Reynolds87}, similar to particle system, agents tend to congregate in a swarming group and there is no contact between individuals, so pushing behavior cannot be simulated.
        Based on cognitive science results, a recent synthesis vision-based steering approach has been proposed \cite{Ondrej:2010:SBS:1778765.1778860}. It does not check collisions explicitly and is not free from overlap, but the proposed approach better simulates the locomotion control of real human.
        %collisions and overlaps
        %which are triggered in certain cases.
        %In conjunction with cognitive models,  The model was firstly introduced in Reynolds' boids system. Agents apply collision detection and avoid colliding with other agents \cite{Pelechano}.
  \item \emph{Geometrical model} explicitly computes geometrical admissible velocities \cite{vandenBerg08}\cite{Berg08}. Every agent chooses its velocity outside the \emph{Reciprocal Velocity Obstacle}, which is calculated by the shape and position information of nearby agents, and thus each agent achieves a collision-free steering. Without psychological factors it is different from how real people steer.
\end{itemize}


